In this work we propose that endoreversible Carnot–type heat engines have a general property independent of the heat transfer law used to describe heat exchanges between the working fluid and its thermal reservoirs. This property has to do with the so-called ecological function [F. Angulo–Brown, J. Appl. Phys. 69, 7465 (1991)]. According to this property, the efficiency at the maximum of the ecological function is the semisum of the Carnot and the maximum power efficiencies for any heat transfer law. This result is obtained by using the quasiparabolic behavior of power versus efficiency. From this property, we obtain a corollary over a general quantitative relation between the power (and also the entropy production) of both maximum power and maximum ecological regimes. We also discuss a criterion to find the best ecological function.

Following the recent proposal by Van den Broeck for a heat engine [Phys. Rev. Lett. 95, 190602 (2005)], we analyze the coefficient of performance of a refrigerator in two working regimes using the tools of linear irreversible thermodynamics. In particular, one of the analyzed regimes gives a coefficient of performance which could be considered as the equivalent to the Curzon-Ahlborn efficiency. Also we consider the relation with the Clausius inequality, and some results for the relevant thermodynamic magnitudes in this formalism are confronted with those obtained using the finite-time thermodynamics framework.

Several authors have shown that dissipative thermal cycle models based on finite-time thermodynamics exhibit loop-shaped curves of power output versus efficiency, such as it occurs with actual dissipative thermal engines. Within the context of first-order irreversible thermodynamics (FOIT), in this work we show that for an energy converter consisting of two coupled fluxes it is also possible to find loop-shaped curves of both power output and the so-called ecological function versus efficiency. In a previous work Stucki [J. W. Stucki, Eur. J. Biochem. 109, 269 (1980)] used a FOIT approach to describe the modes of thermodynamic performance of oxidative phosphorylation involved in adenosine triphosphate (ATP) synthesis within mithochondrias. In that work the author did not use the mentioned loop-shaped curves and he proposed that oxidative phosphorylation operates in a steady state at both minimum entropy production and maximum efficiency simultaneously, by means of a conductance matching condition between extreme states of zero and infinite conductances, respectively. In the present work we show that all Stucki's results about the oxidative phosphorylation energetics can be obtained without the so-called conductance matching condition. On the other hand, we also show that the minimum entropy production state implies both null power output and efficiency and therefore this state is not fulfilled by the oxidative phosphorylation performance. Our results suggest that actual efficiency values of oxidative phosphorylation performance are better described by a mode of operation consisting of the simultaneous maximization of both the so-called ecological function and the efficiency.

In this work it is shown that a general property of endoreversible Curzon-Ahlborn-Novikov (CAN) cycles previously demonstrated can be extended for non-endoreversible CAN-cycles. This general property is based on the fact that at the so-called maximum ecological regime the efficiency is the average of the Carnot and the maximum-power efficiencies, and that in such a regime the power output is 75% of the maximum power of the CAN-cycle and the entropy produced is only 25% of that produced in the maximum power point. This property is independent of the heat transfer law.

In this work, we analyze a nonendoreversible thermal engine model with a nonlinear heat transfer law between the heat reservoirs and the working fluid under two optimization criteria: the maximum power regime and the so-called ecological criterion. We find that this nonendoreversible model has a similar behaviour to that shown by De Vos (Am. J. Phys. 53, 570 (1985)) for endoreversible models with two thermal conductances with only one superior conductance and with only one inferior conductance, respectively. The model is compared with two sets of real power plants, the first one containing power plants of old design (before 1960's) and the second one being formed by modern nuclear power plants. Our results suggest that the first group was designed under conditions which are reminiscent of a maximum power regime and the second one under an ecological-like criterion. We also study some general properties of nonendoreversible thermal engine models.